Accrued Interest and Decomposition of a Reverse Floater
Summary
The document considers accrued interest on a reverse floater whose coupon is linked inversely to a reference rate, subject to a floor at zero. It checks a calculation based on the rate fixed for the next coupon period and the fraction of that period elapsed. The answer highlights a day-count issue: under Act/365, accrued interest would generally use elapsed days divided by 365 times the annualized coupon amount. The proposed fraction of elapsed days over the full coupon period assumes equal weighting of the two six-month periods and corresponds more closely to an Act/365 Fixed treatment.
The post also asks how to represent the security as simpler instruments, including fixed coupon bonds, a floating-rate note, and a cap. The response says decompositions using an out-of-the-money option are often more convenient because the adjustment is smaller; alternative decompositions can be equivalent. The bond prospectus ultimately determines the applicable accrual convention, so the example alone cannot settle the calculation.
Key ideas
- A reverse floater coupon can be expressed as a fixed rate less a reference rate, floored at zero.
- Accrued interest depends on the stated day-count convention.
- Act/365 generally accrues using elapsed days over 365 times the annualized coupon amount.
- Using a fraction of the coupon period assumes equal weighting across the periods.
- An out-of-the-money option can make a reverse floater decomposition adjustment smaller.
Tags
Full text
# How to calculate accrued interest for a reverse floater? # How to calculate accrued interest for a reverse floater? I was looking at an example from my lecture notes regarding a reverse floater. We have the following data (We use the Act/365 convention): - Clean price (02.03.2023): 97,25 - For the reference interest rate we have: 14.04.2022: -0,3% 14.10.2022: 2,1% 14.04.2023: 3,2% I tried to calculate the dirty price at 02.03.2023 myself for a nominal value of $N = 100000$ EUR, but I am not sure if my calculation are correct: The next coupon date will be the 14.04.2023. The reference rate was fixed at the 14.10.2023 and is 2,1%. Therefore, the coupon should be $$ Coupon = N \cdot 0,5 \cdot (4,5\% - 2,1\%)^+ = 1200. $$ I counted a total of 139 days from 15.10.2022 to 02.03.2023. Since there a total of 182 days between the two coupon dates, the accrued interest is $139/182 \cdot 1200 = 916,48$ EUR. And therefore we have a dirty price of $97,25\% \cdot N + 916,48 = 98166,48$ EUR. I am quite new to this and not sure if this is correct. Could somebody verify my calculations? Furthermore the exercise claims, that we can decompose this product into simpler products using 2 long positions in a coupon bond with nominal value $N$ and a coupon of 2,25% each, a short position in a floating rate note with the nominal value $N$ and an interest rate cap with a fixed rate of 4,5%, again with nominal value $N$. What is the thought process behind this decomposition, wouldn't it be much easier to just claim that a floating rate note is just an interest rate floor with fixed leg of 4,5%? ## Answer by dm63 (score 4, accepted) https://quant.stackexchange.com/a/75851 For the coupon calculation, it looks essentially correct. The only caveat is that the day count convention Act/365 usually means the payment would be 139/365 times 2400, rather than 139/182 times 1200. The latter method inherently assumes the coupons in the 2 6 month periods are exactly equal in weight, which I believe is the Act/365 (fixed) convention. However, the bond prospectus would in practice settle the question. On the decomposition, it is usually easier to decompose using an out of the money option, rather than an in the money option (then the adjustment to be made is smaller). Other than that the decompositions are the same. (Did you mean 4.5% rather than 5%).
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